A parcel service to establish a weight value c, beyond which there will be an additional charge. The weight of parcels handled by this service is Normally distributed

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Question: Normal Distribuion Probability

A parcel service to establish a weight value c, beyond which there will be an additional charge. The weight of parcels handled by this service is Normally distributed with a mean of 7 kg and a standard deviation of 2.1 kg.

  1. What value for c (in kg) will insure that only 2.5% of handled package are assessed the additional charge? (Give decimal answer to two places past decimal.)
  2. What value for c (in kg) will insure that only 1.0% of the handled packages are assessed the additional charge? (Give decimal answer to two places past decimal.)

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Given:  Weights of parcels handled by this service is Normally distributed with a   and  and parcel service wants to establish a weight c , beyond which there will be an additional charges.

Part a) We have to find value for c such that , only 2.5% of handled packages are assessed the additional charges.

That is we have to find the value for c such that :

P( X > c ) = 2.5%

P( X > c ) = 0.025

that is : P( X < c ) = 1 – P( X > c )

P( X < c ) = 1 –   0.025

P( X < c ) = 0.9750